Average Error: 6.2 → 1.0
Time: 29.0s
Precision: 64
\[x + \frac{\left(y - x\right) \cdot z}{t}\]
↓
\[\begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 4.21688783645265377 \cdot 10^{-84}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]
x + \frac{\left(y - x\right) \cdot z}{t}
↓
\begin{array}{l}
\mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 4.21688783645265377 \cdot 10^{-84}\right):\\
\;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\

\mathbf{else}:\\
\;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\

\end{array}
double f(double x, double y, double z, double t) {
        double r580367 = x;
        double r580368 = y;
        double r580369 = r580368 - r580367;
        double r580370 = z;
        double r580371 = r580369 * r580370;
        double r580372 = t;
        double r580373 = r580371 / r580372;
        double r580374 = r580367 + r580373;
        return r580374;
}
↓
double f(double x, double y, double z, double t) {
        double r580375 = x;
        double r580376 = y;
        double r580377 = r580376 - r580375;
        double r580378 = z;
        double r580379 = r580377 * r580378;
        double r580380 = t;
        double r580381 = r580379 / r580380;
        double r580382 = r580375 + r580381;
        double r580383 = -inf.0;
        bool r580384 = r580382 <= r580383;
        double r580385 = 4.216887836452654e-84;
        bool r580386 = r580382 <= r580385;
        double r580387 = !r580386;
        bool r580388 = r580384 || r580387;
        double r580389 = r580380 / r580378;
        double r580390 = r580377 / r580389;
        double r580391 = r580375 + r580390;
        double r580392 = r580388 ? r580391 : r580382;
        return r580392;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original6.2
Target2.0
Herbie1.0
\[\begin{array}{l} \mathbf{if}\;x \lt -9.0255111955330046 \cdot 10^{-135}:\\ \;\;\;\;x - \frac{z}{t} \cdot \left(x - y\right)\\ \mathbf{elif}\;x \lt 4.2750321637007147 \cdot 10^{-250}:\\ \;\;\;\;x + \frac{y - x}{t} \cdot z\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \end{array}\]

Derivation

  1. Split input into 2 regimes

  2. if (+ x (/ (* (- y x) z) t)) < -inf.0 or 4.216887836452654e-84 < (+ x (/ (* (- y x) z) t))

    1. Initial program 12.8

      \[x + \frac{\left(y - x\right) \cdot z}{t}\]
    2. Using strategy rm

    3. Applied associate-/l*1.4

      \[\leadsto x + \color{blue}{\frac{y - x}{\frac{t}{z}}}\]

    if -inf.0 < (+ x (/ (* (- y x) z) t)) < 4.216887836452654e-84

    1. Initial program 0.7

      \[x + \frac{\left(y - x\right) \cdot z}{t}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.0

    \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{\left(y - x\right) \cdot z}{t} = -\infty \lor \neg \left(x + \frac{\left(y - x\right) \cdot z}{t} \le 4.21688783645265377 \cdot 10^{-84}\right):\\ \;\;\;\;x + \frac{y - x}{\frac{t}{z}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(y - x\right) \cdot z}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x y z t)
  :name "Numeric.Histogram:binBounds from Chart-1.5.3"
  :precision binary64

  :herbie-target
  (if (< x -9.025511195533005e-135) (- x (* (/ z t) (- x y))) (if (< x 4.275032163700715e-250) (+ x (* (/ (- y x) t) z)) (+ x (/ (- y x) (/ t z)))))

  (+ x (/ (* (- y x) z) t)))